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Commit2d1bd71f6be8caec07282163138af6f56187a295 (patch)
Author
 Syndamia <kamen.d.mladenov@protonmail.com>
2021-11-10 00:00:58 +0200
Committer
 Syndamia <kamen.d.mladenov@protonmail.com>
2021-11-10 00:00:58 +0200
Files988cc649ee3d97be13f493bad190c121bdab90f8
uni-projects-2d1bd71f6be8caec07282163138af6f56187a295.tar
uni-projects-2d1bd71f6be8caec07282163138af6f56187a295.tar.gz
uni-projects-2d1bd71f6be8caec07282163138af6f56187a295.zip
Parent116e8d7807f32a96a682e4530fb5ef802a8e3d57 (diff)
Fixed bad punctuation
2 files changed, 2 insertions, 2 deletions
-rw-r--r--Year 1/Mathematical analysis/Homework1.pdfbin40673 -> 40670 bytes
-rw-r--r--Year 1/Mathematical analysis/Homework1.tex4
diff --git a/Year 1/Mathematical analysis/Homework1.pdf b/Year 1/Mathematical analysis/Homework1.pdf
index e1a3345..d55e677 100644
--- a/Year 1/Mathematical analysis/Homework1.pdf
+++ b/Year 1/Mathematical analysis/Homework1.pdf
Binary files differ
diff --git a/Year 1/Mathematical analysis/Homework1.tex b/Year 1/Mathematical analysis/Homework1.tex
index 4514496..08027dc 100644
--- a/Year 1/Mathematical analysis/Homework1.tex
+++ b/Year 1/Mathematical analysis/Homework1.tex
@@ -74,11 +74,11 @@
\begin{align*}
& \arcsin \left( 2x \sqrt{1-x^2} \right) = \alpha \iff \sin \left( \alpha \right) = 2x \sqrt{1-x^2} \qquad \arccos \left( x \right) = \beta \iff \cos \left( \beta \right) = x \\
& \text{За } x = \frac{-\sqrt{2}}{2} \;,\quad \sin(\alpha) = \cancel{2} \cdot \frac{-\sqrt{2}}{\cancel{2}} \cdot \sqrt{1 - \left( \frac{-\sqrt{2}}{2} \right)^2} = -\sqrt{2} \cdot \sqrt{\frac{1}{2}} = -1 \;,\; \cos \left( \beta \right) = -\frac{\sqrt{2}}{2} \\
- & \text{Аналогично, за } x = \frac{\sqrt{2}}{2} \;,\quad \sin \left( \alpha \right) = 1 \;,\quad \cos \left( \beta \right) = \frac{\sqrt{2}}{2} \\
+ & \text{Аналогично за } x = \frac{\sqrt{2}}{2} \;,\quad \sin \left( \alpha \right) = 1 \;,\quad \cos \left( \beta \right) = \frac{\sqrt{2}}{2} \\
& \implies \alpha \in \left[ -\frac{\pi}{2}, \frac{\pi}{2} \right] \;,\; \beta \in \left[ -\frac{\pi}{4}, \frac{\pi}{4} \right] \implies \sin \left( \beta \right) = +\sqrt{1 - \cos ^ 2 \left( \beta \right)} = \sqrt{1 - x ^ 2} \\
& \omit\hfill \\
& \sin \left( \alpha \right) = 2x\sqrt{1 - x^2} = 2\cos \left( \beta \right)\sin \left( \beta \right) = \sin \left( 2\beta \right) = \sin \left( \pi - 2\beta \right) \qquad\quad 2\beta \in \left[ -\frac{\pi}{2}, \frac{\pi}{2} \right] \\
- & \colorbox{yellow}{$\implies \alpha = \pi - 2\beta$}
+ & \implies \colorbox{yellow}{$\alpha = \pi - 2\beta$}
\end{align*}
\hfill